[time-nuts] Frequency standards for different tau in Allen Dev measurement

[Magnus Danielson]

Hi Taka,

On 2020-02-22 04:55, Taka Kamiya via time-nuts wrote:
> It's not like drinking from a fire hydrant.  It's like drowning in hoover dam, get sucked into an inlet, pulverized by turbine blade, and getting spit out into a stream.  
Hmm, not exactly what I had hoped for as your experience... whatever,
hope it is worth it.
>
> One question :  
>
> You said this: 
> "The resolution of your counter tells you about where your 1/tau curve
> will cut tau = 1 s, and it goes from there. There is a slight scaling
> factor, but if we assume it is 1 for now, it is pretty simple. Your
> 5335A has 1 ns single-shot resolution, this gives 1E-9 at 1 s, but 1E-10
> at 10 s, 1E-11 at 100 s and 1E-12 at 1000 s. You see very clearly when
> the linear slope ends and "lands" in the noise, at which time the noise
> becomes dominant and is giving you the interesting reading."
> By using the same logic, I can keep going up and up on longer gate time and tau keeps getting better and better.  I know at one point, inflection happens and that indicates noise taking over.  But what kind of noise (phase?) and how does that happen?

OK. Good question.

The instrument noise in itself can be while phase noise and flicker
phase noise. The resolution limit will be a systematic disturbance. All
these three has the same 1/tau slope so from these three, nothing
happens as tau increases. At some point naturally will thermal
instability come in, but that will be another systematic, but it will be
hard to cancel. So that is the limit of the instrument.

However, the noise of the reference and DUT will dominate for larger
taus, and thus it will be good enough to measure that noise. Besides,
length of measurement becomes a limit.

>   Only thing that changes in this equation is the gate time.  Everything is constant.  You mean gate time is no longer accurate enough to support the minute shift in phase?
> I'm still confused about the precision (not accuracy) of the time base.  Am I still ultimately constrained by this?
There are ways to get around it.
>   Without DMTD, or some kind of pre-scaling of DUT, if I measure Rb with time base using another Rb, they are both rubber-bands, correct?
Now, what you can do is to do a three-cornered hat measurement.
Essentially you measure three sources at once as three pair-wise
measurements. You calculate your ADEV of each pair. Now, as you have the
noises n1, n2 and n3 of each source, measurement m1 = n1+n2, m2 = n1+n3
and m3 = n2+n3. This equation problem can be solved to bring out n1, n2
and n3 separate. The trouble is, this does not always work out as
precisely as one would like, because the measurements isn't precise and
well converged. Therefore it is a bit of sensitive process, but if one
gets it working, you can achieve the separation.
> I'm infinitely curious by nature.  I need to know everything, even to a minute detail, to be satisfied.  I hope you don't get tired of this.    

So far, you ask relevant questions that can be given an answer. Being a
curious person myself, I've digged down.

Cheers,
Magnus